The work to swing limbs in humans versus chimpanzees and its relation to the metabolic cost of walking

Compared to their closest ape relatives, humans walk bipedally with lower metabolic cost (C) and less mechanical work to move their body center of mass (external mechanical work, WEXT). However, differences in WEXT are not large enough to explain the observed lower C: humans may also do less work to move limbs relative to their body center of mass (internal kinetic mechanical work, WINT,k). From published data, we estimated differences in WINT,k, total mechanical work (WTOT), and efficiency between humans and chimpanzees walking bipedally. Estimated WINT,k is ~ 60% lower in humans due to changes in limb mass distribution, lower stride frequency and duty factor. When summing WINT,k to WEXT, between-species differences in efficiency are smaller than those in C; variations in WTOT correlate with between-species, but not within-species, differences in C. These results partially support the hypothesis that the low cost of human walking is due to the concerted low WINT,k and WEXT.


Internal kinetic mechanical work
Experimental measurements of W INT,k are unavailable for chimpanzees.However, in legged animals, W INT,k (J kg −1 m −1 ) can be modeled as 28 : where SF is the stride frequency (Hz), v is the average progression speed (m s −1 ), d is the duty factor, and q is a dimensionless term that depends on the inertial properties of the limbs: (1) Demographic and biometric characteristics of the study participants.For Demes et al. 6 , no information could be retrieved about sex.where a and γ are the average proximal distance and gyration radius of the lower limb center of mass as a fraction of limb length, b is the upper limb length as a fraction of the lower one, and m' L and m' U are the masses as a fraction of body mass of the lower and upper limbs, respectively 28 .This equation neglects differences in relative gyration radius between upper and lower limbs, which may be inappropriate when comparing W INT,k between species since the proportional mass distribution between fore-and hindlimbs differs between humans and chimpanzees 24,26,30,31 .A more general version of Eqs.
(1) and ( 2) can be written from the original formulation by Minetti and Saibene 32 : where Ẇ INT,k is the mechanical internal power, and γ L and γ U are the gyration radii of the lower and upper limbs as a fraction of the respective limb length.To account for the duty factor, v 2 can be written as 28 : where v ST is the progression speed term, and v SW is the term for the limb speed relative to the body center of mass.The relation between v SW and the duty factor (d) is given by: Combining ( 4) and ( 5) yields: Defining m' L and m' U as the fractional masses of the upper and lower limbs, and m as the total body mass: Converting from mechanical power to the mechanical work performed to move a unit body mass per unit distance (J kg −1 m −1 ): This equation only differs from the equation presented in the work of Minetti 28 in that it does not assume equal relative gyration radii for the upper and lower limbs.The term q' can be defined here as: For which q is a special case when a unique radius of gyration relative to limb length (γ) is assumed for the upper and lower limbs (γ L = γ U = γ).Hence: This allowed estimating W INT,k for chimpanzees based on spatiotemporal data from Pontzer et al. 2 ; for humans, W INT,k values were taken from Pavei et al. 29 .This model assumes extended limbs but can be expanded to account for the bent-hip, bent-knee features of chimpanzees walking; the validity of such mechanical work estimates is discussed in Supplementary Material S1.
In addition to W INT,k , work is done to overcome joint frictions during locomotion (internal frictional mechanical work, W INT,f ; J kg −1 m −1 ) 33 ; this term is not estimated here for chimpanzees because experimental data on limb damping are lacking (Supplementary Material S2).

External mechanical work and total mechanical work
For humans, external mechanical work (W EXT ) increases with walking speed 12,20,29 ; however, for chimpanzees, such a relationship is less clear.Here W EXT data for chimpanzees walking bipedally were taken from Demes et al. 6 and fitted with zero, first-and second-order mixed effect models in the forms: www.nature.com/scientificreports/where β and b are the fixed and random effect coefficients, respectively.The Akaike Information Criterion (AIC) was calculated, and the model with the lowest AIC was chosen.A zero-order model had the lowest AIC (Supplementary Material S3), so all the analyses in the present work used a speed-independent value of 0.55 ± 0.18 J kg −1 m −1 , equal to the mean W EXT reported by Demes and colleagues 6 .All these analyses were done with R 3.6.2,R Studio 1.2, and lme4 [34][35][36] .W TOT was then calculated as the sum of W INT,k and W EXT , and its standard deviation as 37 : where SD WINT,k and SD WEXT are the standard deviations for W INT,k and W EXT , respectively.For humans, experimental values for W INT,k , W EXT and W TOT were taken from Pavei et al. 29 .

Stride frequency and duty factor
For each species, stride frequency and duty factor values from Pavei et al. 29 and Pontzer et al. 2 were regressed over speed (Fig. 1).Then, percent variations were calculated from regression equations at the minimum (0.45 m s −1 ) and maximum (1.67 m s −1 ) common speeds between the two datasets and reported in Table 2.The uncertainties for SF and d were quantified by their standard deviations SD SF and SD d , and propagated as:  11) are plotted for chimpanzees (red circles; data from Pontzer et al. 2 ) and humans (blue squares; data from Pavei et al. 29 ).Species-specific linear and polynomial regression equations are shown, together with their coefficient of determination (R 2 ).
Table 2. Determinants of W INT,k .Human parameters were calculated from De Leva et al. 23 and Pavei et al. 29 , mean of females and males.Parameters for chimpanzees were calculated from Druelle et al. 39 and Pontzer et al. 2 , mean of females and males.For spatiotemporal parameters, brackets report the minimum and maximum values and percent variations in the common speed range (0.45-1.67 m s −1 ).reported similar duty factors between three chimpanzees and three speed-matched humans.Despite this, duty factor values from the former study were chosen due to the larger number of chimpanzee participants and a wider range of walking speeds.In instances of smaller differences in duty factor, the resulting differences in W INT,k would be smaller but still be present, as indicated by error propagation and Table 2.

Metabolic cost and efficiency
To calculate efficiency, metabolic demands must be expressed in the same units as mechanical ones.Pontzer et al. 2 measured the oxygen uptake of five chimpanzees walking bipedally on a treadmill at various speeds.From these data, metabolic cost C (J kg −1 m −1 ) can be calculated as 40,41 : where VȮ 2ss and VȮ 2rest are the oxygen uptake during steady-state locomotion and at rest, respectively, m is the body mass (kg), and EqO 2 is the number of joules released during the combustion of one milliliter of oxygen.EqO 2 spans from 19.62 to 21.13 J mLO 2 -142 , and here a mean value of 20.9 J per mLO 2 is assumed.Efficiency is W TOT C −121 ; therefore, its standard deviation is given by 37 : where SD C is the sample standard deviation for C. For humans, Pavei and colleagues 29 provide experimental measurements of C and efficiency.Each outcome variable was regressed over speed; due to the small sample size and the unsuitability of null hypothesis testing for such a study design, only regression parameters were reported together with their coefficient of determination (R 2 ).

Results
Compared with chimpanzees, humans have lower stride frequency and duty factor at all speeds, and a lower q' (Fig. 1, Table 2), leading to lower W INT,k (Fig. 2).In the common speed range 1.1-1.4m s −1 , W EXT ranges from 0.46 to 0.55 J kg −1 m −1 for humans and averages 0.55 J kg −1 m −1 for chimpanzees.Because of concomitantly decreased W INT,k and W EXT , humans walk with less W TOT than chimpanzees (Fig. 2, Supplementary Fig. S4).As values of C from humans are proportionally lower than those of chimpanzees at all speeds, between-species differences in efficiency are smaller than differences in either C or W TOT (Fig. 2, Supplementary Fig. S4).

Discussion
In this paper, we provide evidence that humans walk bipedally with less mechanical internal work than chimpanzees.Total mechanical work is also lower in humans than in chimpanzees, making between-species differences in efficiency smaller than those in metabolic cost.

Mechanical work
At a given speed, W INT,k is proportional to three terms: stride frequency, a monotonous function of duty factor, and an 'inertial term' that lumps relative limb lengths and masses distribution 28 (Eq.1).Such a model is coherent with stereophotogrammetric calculations of W INT,k 22,44 , and explains the mechanisms driving changes in W INT,k between and within species 28,29,45 ; however, it assumes equal relative gyration radii and center of mass position for all limbs.As limb mass distribution differs between chimpanzees and humans, we generalized such model to avoid these assumptions (Eqs.10 and 11).The model also assumes fully extended limbs, but Supplementary Material S1 and Fig. 3 show that limb flexion would not relevantly alter calculations of mechanical work and efficiency.In the range of speeds between 0.45 and 1.67 m s −1 , humans walk with a lower stride frequency 2,29 , contributing to a 22-25% reduction in estimated W INT,k (Table 2, Fig. 1); humans also have a lower duty factor at low speeds (which further reduces W INT,k by up to 49%), but this difference diminishes at higher speeds (Table 2, Supplementary Fig. S4).Even if the human upper limb has a greater relative gyration radius than chimpanzees' forelimb, this is compensated by its lower fractional mass and length (Table 2) 23,24 ; altogether, this reduces q', and hence W INT,k by an additional 16%.As a result, humans have a ~ 60% lower W INT,k than chimpanzees.These different strategies may reflect distinct optimization goals in the two species: a higher duty factor and stride frequency may optimize safety and stability in chimpanzees, while lowering them curbs the mechanical demands of walking in humans; greater distal masses in the upper limbs favor climbing and brachiation, while shifting them proximally and to the lower limbs reduces the cost of walking 46 .
Besides W INT,k , work is done to overcome joint friction during locomotion (W INT,f ) 33 .Generalizing its formula, W INT,f is proportional to , where β U , β L , R U, R L are the damping coefficients (N m s rad −1 ) and length (m) of the upper and lower limbs, respectively (Supplementary Material S2).If human damping coefficients β U and β L are taken from Minetti et al. 33 and the same are assumed for chimpanzees, humans would do less W INT,f because of the concomitantly increased R U and R L .However, this assumption is challenged by the interspecies differences in soft tissue distribution and anatomy of the proximal limb joints 47 , potentially causing ( 16) Vol:.( 1234567890 great differences in damping coefficients.Therefore, W INT,f was not quantified here or included in W TOT ; this quantity however should not be negligible, and once data on damping become available, estimates of mechanical work in chimpanzees could be improved.Finally, the interplay between W EXT and W INT,k is not solved yet: summing them could be considered an "upper bound" estimate of whole-body mechanical work 48,49 and their metabolic correlate may seem counterintuitive since C of human walking increases when people are not allowed to swing their arms 50 .However, the fact that the net effect of removing upper limb swing increases C does not imply that limb swing happens at no metabolic cost.On the contrary, muscle blood flow measurements in animal and modeling studies 51,52 , the existence of dissipation between and within joints 33 and the fact that W INT,f values in humans are of the same magnitude as  29 for humans.Error bars: standard deviation.Solid lines: regression lines for chimpanzees (red) and humans (blue).Shaded area in panel (d): maximum efficiency range for isolated muscles contracting concentrically 43 .
Figure Mechanical work and efficiency assuming a flexed hindlimb.In addition to the data presented in Fig. 2, this plot shows how assuming a flexed lower limb for chimpanzees impacts modeled W INT,k , W TOT , and efficiency.In the flexed limb model, a mean knee flexion angle of 125° (with 180° representing knee full extension) and a mean angle of the foot relative to the vertical of 80° was considered (see Supplementary Material S1).Error bars: standard deviation.those of W INT,k themselves 33 challenge the idea that limb swing can happen at negligible cost and that calculations of limb swing costs can be ignored.Further models should also include the effect of natural limb oscillation frequency 48,53,54 and W INT,f 33 on C.

Locomotor efficiency
Due to the lower W EXT 6 and W INT,k , humans had a lower W TOT : consequently, the disparities in locomotor efficiency between the two species were considerably smaller than those in C (Fig. 2).While this suggests that a portion of the lower C in humans can be attributed to reduced mechanical work, the extant differences in efficiency between the two species hint that mechanical work does not explain all variations in C.Moreover, efficiency was speed-dependent (Fig. 2); for chimpanzees, this was due to the fact that W EXT and C were approximately constant, while W INT,k increased with speed.Finally, differences in W TOT are less pronounced when comparisons are done at dynamically similar speeds (Supplementary Fig. S4).
Locomotor efficiency can also be expressed as the product of muscle efficiency and transmission efficiency 55 , and humans may have optimized both components.Muscle efficiency may be enhanced due to optimized muscle architecture and a higher proportion of type I fibers 1,4,56 ; it also increases when muscles operate at advantageous velocities 43,57,58 , but data are lacking for chimpanzees walking.On the other hand, transmission efficiency increases when elastic energy is stored and released in the tendons and connective tissues of the hip, ankle, and foot [59][60][61][62][63][64] ; this can result in overall ("apparent") efficiency being higher than that of isolated muscle (Fig. 2).Such a hypothesis is supported by observations by O'Neill and colleagues 19 who found that humans, but not chimpanzees, can save a relevant fraction of mechanical work during a stride through elastic mechanisms; this could account for some of the remaining between-species differences in efficiency in Fig. 2. When using mechanical work data from O'Neill and colleagues 19 to compute locomotor efficiency, we found values of 0.23 for chimpanzees and 0.37 for humans walking at 1.09 m s −1 (Supplementary Material S5).O'Neill et al. 19 also estimated how much work humans could save due to elastic mechanisms: by subtracting it from total mechanical work, a "muscle" efficiency of 0.25 is derived.At the same speed, our efficiency estimates are 0.22 for chimpanzees and 0.29 for humans (Supplementary Material S5).This suggests numerical consistency between the present results and those from O'Neill and colleagues 19 and that the remaining discrepancies in locomotor efficiency between species can be attributed to factors not captured by mechanical work calculations, including optimized muscle-tendon mechanics in humans.Transmission efficiency also improves when muscles operate at advantageous lengths and moment arms, and with reduced lower limb co-contractions 55 : both mechanisms may contribute to reducing C in humans thanks to their ability to walk with more extended hips and knees 1, 65 .In contrast, the pelvis orientation in chimpanzees forces them to keep these joints bent during the stance phase 3,14,65 , likely at the cost of increased isometric contraction of lower limb muscles.This can increase C without affecting W EXT .Transmission efficiency also depends on belly and tendon gearing 66 and soft tissue deformations 19,67 ; further studies are needed to elucidate their role in the comparative physiology of walking.

Limitations and future perspectives
This work relies on published data to estimate differences in W INT,k, between humans and chimpanzees and generate hypotheses on how they affect the cost of walking.The present is an analytical estimate of W INT,k : the model can yield reasonable estimates since it holds for a range of gaits, speeds, and species 28,44,45 , but experiments are needed to measure W INT,k in chimpanzees and test these hypotheses by collecting mechanical and metabolic data on the same participants.Experimental measures would also show whether mediolateral movements, which are neglected in this model but are potentially relevant for chimpanzees, affect internal work calculations.Of note, experimental data on W EXT and C come from adult chimpanzees with heterogeneous age and biometry (Table 1); however, chimpanzees' walking mechanics does not relevantly change after the age of 5 years 68 .
On one hand, further experiments are required to measure quantities that could refine estimates of mechanical work in chimpanzees, including the precise amount of external work done during the double support phase 69,70 , the mechanical work actually performed at the muscle level 71,72 , and tendon elastic storage and recoil, which would require combined ultrasound and kinetic data 59 .On the other hand, between-species differences in metabolic cost have also been addressed by force-based rather than work-based models 3,53,73 ; future work may elucidate whether these two contributions are mutually exclusive, additive 74 or equivalent 75 .

Conclusions
Compared to chimpanzees, the lower cost of human walking is associated with a combined reduction in the work to accelerate and raise their body center of mass and the work to swing their limbs.When both terms are considered, estimated walking efficiency is still higher in humans than chimpanzees, suggesting that factors beyond mechanical work also contribute to such differences in metabolic cost between the two species.

Figure 2 .
Figure 2. Mechanical work, metabolic cost, and efficiency.Internal kinetic mechanical work (W INT,k ), total mechanical work (W TOT ), metabolic cost, and locomotor efficiency are plotted as a function of speed.Data from Pavei et al.29 for humans.Error bars: standard deviation.Solid lines: regression lines for chimpanzees (red) and humans (blue).Shaded area in panel (d): maximum efficiency range for isolated muscles contracting concentrically43 .